Mathematical Sciences: Algebraic Methods in Systems Theory

9300805罗森塔尔这个项目解决了系统论、插值论和编码理论中的许多问题，所有这些问题都涉及所有有界次自回归系统的代数性质。研究的主要目的是改进稳定动态反馈补偿器的设计方法，更好地理解传递函数空间的稳健性和拓扑性质之间的相互作用，以及构造低复杂度和大自由距离的卷积码的新方法。许多现实世界的系统可以由所谓的线性系统进行数学建模。线性系统的两个例子是在反馈控制器的设计中广泛使用的动态反馈补偿器，以及在许多数据传输方案中实现的卷积编码器和解码器。这个项目的目标是发展一种数学理论，从而改进各种类型的反馈控制器的设计技术，以及更有效的卷积编码器和解码器。***

9300805 Rosenthal This project addresses a number of issues in systems theory, interpolation theory and coding theory, all of which involve algebraic properties of the class of all autoregressive systems of a bounded degree. The main objectives of the research are improved methods for the design of stabilizing dynamic feedback compensators, a better understanding of the interplay between issues of robustness and topological properties of the space of transfer functions, and new methods for constructing classes of convolutional codes with a low complexity and a large free distance. Many real world systems may be mathematically modeled by so- called linear systems. Two examples of a linear system are dynamic feedback compensators, which are widely used in the design of feedback controllers, and convolutional encoders and decoders, which are implemented in many data transmission schemes. It is the goal of this project to develop a mathematical theory which will lead to improved design techniques for feedback controllers of various types as well as more efficient convolutional encoders and decoders. ***